If |z₁ |=2, |z₂ |=3, |z₃ |=4 and |2 z₁+3 z₂+4 z₃ |= 4 , then absolute value of 8 z₂ z₃+27 z₃ z₁+64 z₁ z₂ equals

Step-by-step solution

|8 z₂ z₃+27 z₃ z₁+64 z₁ z₂ |= |z₁ | |z₂ | |z₃ | | 8 z₁ + 27 z₂ + 64 z₃ |=(2)(3)(4) | 8 z ₁ |z₁ |^2 + 27 z ₂ |z₂ |^2 + 64 z ₃ |z₃ |^2 |=24 |2 z ₁+3 z ₂+4 z ₃ |=24 | 2 z₁+3 z₂+4 z₃ |=24 |2 z₁+3 z₂+4 z₃ |=(24)(4)=96